Comprehensive investigation of material properties and operational parameters for enhancing performance and stability of FASnI3-based perovskite solar cells

Recent advancements in the efficiency of lead-based halide perovskite solar cells (PSCs), exceeding 25%, have raised concerns about their toxicity and suitability for mass commercialization. As a result, tin-based PSCs have emerged as attractive alternatives. Among diverse types of tin-based PSCs, organic–inorganic metal halide materials, particularly FASnI3 stands out for high efficiency, remarkable stability, low-cost, and straightforward solution-based fabrication process. In this work, we modelled the performance of FASnI3 PSCs with four different hole transporting materials (Spiro-OMeTAD, Cu2O, CuI, and CuSCN) using SCAPS-1D program. Compared to the initial structure of Ag/Spiro-OMeTAD/FASnI3/TiO2/FTO, analysis on current–voltage and quantum efficiency characteristics identified Cu2O as an ideal hole transport material. Optimizing device output involved exploring the thickness of the FASnI3 layer, defect density states, light reflection/transmission at the back and front metal contacts, effects of metal work function, and operational temperature. Maximum performance and high stability have been achieved, where an open-circuit voltage of 1.16 V, and a high short-circuit current density of 31.70 mA/cm2 were obtained. Further study on charge carriers capture cross-section demonstrated a PCE of 32.47% and FF of 88.53% at a selected capture cross-section of electrons and holes of 1022 cm2. This work aims to guide researchers for building and manufacturing perovskite solar cells that are more stable with moderate thickness, more effective, and economically feasible.

One of the ways to address the increasing global energy demands resulting from extensive infrastructure development is through investment in solar cell technology, where sunlight is converted into electricity using a photovoltaic cell.As a result, the production of solar cells experiences an average biannual increase.The structure of solar cells typically comprises a perovskite layer, where the absorption of light generates most charge carriers within the device.After the absorber layer, transport layers for holes and electrons facilitate the movement of formerly produced charge carriers directed at the anode and cathode 1 .These layers play a crucial role as they significantly contribute to the performance of solar devices.
Organic-inorganic metal halide perovskite solar cells (PSCs) have received significant attention among various solar cell technologies since firstly reported in 2009 by Miyasaka 2 .Their power conversion efficiency has rapidly increased from 3 to 24%, approaching the efficiency of silicon technology, which stands at around 27% 3,4 .Thanks to the unique structure of perovskite materials employing the ABX 3 formula, where A represents the larger cation of either inorganic (alkali metal Cs + ) or organic (CH 3 NH 3 + , MA or HC(NH 2 ) 2 + , FA) nature, B is the smaller divalent metal cation ( Pb 2+ , Sn 2+ , or Ge 2+ ) and X denotes a single halide anion or mixture ( F − , Cl − , Br − , or I − ) 2 .Careful choices of these cations and anions can improve device efficiency and stability.Bhattarai

SCAPS-1D software
The analysis of optoelectrical modelling and photovoltaic characteristics involves utilizing SCAPS software.This reliable program has recently gained popularity within the photovoltaic community for modelling perovskite devices, and the obtained output aligns well with experimental data 21 .An inherent electric field normal to the interfaces is induced by the alignment of energy levels at the interfaces caused by the asymmetric designs of devices, which result in a work function offset between the anode and cathode.This arrangement helps charge carriers drift, making collecting them at electrode contacts easier 22,23 .
There are supposed to be neutral defects at the mid-band gap level in the model, with a Gaussian distribution and a characteristic energy level of 0.10 eV.Cell performance is assessed by utilizing the Shockley-Read-Hall (SRH) recombination model to thoroughly analyze the effects of defect density ( N T ) and capture cross sections ( σ n,p ) for charge carriers at the interface and bulk levels of the absorber layer.The following describes the SRH recombination model 24 .
The σ n,p is contingent on their lifetime ( τ n,p ) before undergoing recombination to form an exciton, as expressed below: The symbols p and n represent the densities of electrons and holes under non-equilibrium conditions.The intrinsic density (n i ), intrinsic energy level (E i ), energy level of trap defects (E t ), and thermal velocity of electrons and holes (v th ) are the characteristics that are used to evaluate the performance of solar cells.These characteristics include fill factor (FF), power conversion efficiency (PCE), short-circuit current density (J sc ), open-circuit voltage (V oc ), quantum efficiency (QE), and current-voltage (J-V) 25 .
where i o represents the dark saturation current.
The following formula can be used to estimate the V oc 26 : where (kt/q) is the thermal voltage and a is factor.The non-radiative and radiative recombination occurring in the primary exciton production zone determines the EQE, which is represented as: where J o,rad−bi indicates the background current density arising from the radiative part of molecular recom- bination, J o,nr−bi indicates the background current density originating from the nonradiative part of molecu- lar recombination, and J o,nr−trap indicates the background current density linked to non-radiative trapassisted recombination.

Structure of FASnI 3 -based perovskite solar cells
As highlighted in the introduction ABX 3 general formula, utilizing inorganic-organic absorber layers in perovskite devices presents a significant challenge related to their long-term operational stability.This concern extends to the material phase stability of the device during its preparation, growth, and synthesis with the risk of limiting large-scale production.The low phase stability observed in organic-inorganic perovskite crystals is typically associated with the halide component 27,28 .This rationale supports the selection of formamidinium (FA) or ethyl-ammonium organic cations similar to the conventional property of common methylammonium (MA) 29,30 .Introducing FA into MA-based perovskite has resulted in notable thermal and environmental stability improvements and enhanced device performance.In addressing toxicity concerns, the divalent tin cation (Sn +2 ) has garnered attention as a practical substitute for the unstable and hazardous lead (Pb).However, one drawback of Sn-based devices is their susceptibility to rapid oxidation, wherein Sn +2 readily oxidizes to Sn +4 upon exposure to air, resulting in swift degradation of cell properties 31,32 .Compared to Pb +2 , Sn +2 has a smaller atomic diameter, improved conductivity, and the capability to form stable perovskite structures.Shao et al. reported high stability with maximum performance of Sn-based PSC and the highest reproducibility achieved 33,34 .
A high-quality FASnI 3 layer with uniform surface morphology and excellent crystallinity is possible through various deposition techniques, including chemical solution deposition, co-evaporation deposition and vaporchemical solution deposition 14,35 .In this work, however, the structure of FASnI 3 -based PSCs, modelled using SCAPS, is FTO/TiO 2 /FASnI 3 /HTL/Ag, where TiO 2 is the electron transport layer (ETL), FASnI 3 is the absorber material, HTL is the hole transporting layer, and Ag is the anode.

Device modelling
First, four different hole transporting materials (HTM) were employed due to their similar electronic and optical properties.These included Spiro-OMeTAD, CuI, Cu 2 O, and CuSCN.However, the initial proposed device was based on Spiro-OMeTAD.It had the following configuration of FTO/TiO 2 /FASnI 3 /Spiro-OMeTAD/Ag, as shown in Fig. 1a, while Fig. 1b showed its energy band diagram.Input parameters of the initial structure were taken from the literature and shown in Table 1.Other HTMs had also similar device configurations with input parameters listed in Table 2.
Second, other parameters like thickness of the active layer, the work function of metal back contact were varied and investigated.Third, the ETL/FASnI 3 and FASnI 3 /HTL interfaces were simulated via varying capture cross-sections for electrons and holes, structural and interface defect density states, which were assumed to account for both structural and interface recombination ratio.Neglecting these interfaces could result in erratic outcomes due to high discontinuity between the absorber layer and ETL/HTL.Optimization calculations were then performed, simulating the effects of front and back contacts on light transmission and reflection.Finally, the diagram of energy band levels was drawn for the optimized FASnI 3 PSCs.www.nature.com/scientificreports/ The effects of all previous parameters were evaluated by analyzing the evolution of J-V and QE properties.It should be noted that every simulation was run with 1000 Wm -2 of external light at 1.5 G AM and 300 K operational temperature.The electron and hole thermal velocities were both set at 10 7 cm/s.With a Gaussian distribution, defects were regarded as neutral 36 .

Effect of different hole transporting materials
In solar cell structure, the hole transporting material (HTM) serves two primary functions: (1) giving the photogenerated holes in the active layer a reachable energy level to enable quick transport throughout the circuit, avoid recombination, and (2) preventing electrons that are rejected by an energy barrier that is high enough.The material selected for the HTL has a substantial impact on cell performance since holes determine the p-type conductivity of perovskite.When selecting the appropriate HTM, key features consist of the valence band states, charge carrier density, dielectric constant, and energy gap.Numerous studies have investigated the impact of HTL on photovoltaic outputs.This section uses a relative analysis to evaluate the influence of incorporating various hole transport materials on current-voltage and external quantum characteristics.In the initial cell employs Spiro-OMeTAD, while the other three structures use CuSCN, CuI and Cu 2 O, with key property values summarized in Table 2. Figure 2 shows that the structure incorporating Cu 2 O as the HTM demonstrates superior performance, as depicted by its current-voltage curve, which has the greatest mean power.Furthermore, Table 3 indicates that the optimal performances, with PCE of 27.13% and FF of 86.08%, are achieved.The hole mobility, with a magnitude of 80 cm 2 /Vs, is approximately 2000 times larger than that of SPO, explaining the increased hole flow.Additionally, its dielectric constant (7.50 eV) is greater than two times of SPO, influencing the strength between charge carriers and contributing to the high hole mobility.Since the HTL has a smaller energy gap (2.17 eV) than SPO (2.88 eV) and the maximum range of incident light reaching it, has less of an impact on QE.It only marginally contributes to the formation of carriers 39,40 .Consequently, the QE curves of all cells are all overlapping.

Effect of absorber layer thickness
Perovskite cells are categorized as thin film devices, typically featuring an active layer thickness in the moderate range with maximum light absorption.They are recognized for achieving high yields even with a thin layer.As illustrated in Fig. 3, this is evident in the progression of J-V curves.Figure 4 shows the performance of PSCs with changing the perovskite layer thickness from 0.1 to 1.8 µm.Particularly, the most efficient devices are observed within the active layer thickness range of 1.5-1.7 µm, based on J-V curves exhibiting the maximum mean power (P m = I m × V m ).We were able to choose 1.6 µm in the further simulations.
The effectiveness of these devices within this thickness range is attributed to the extended duration of light within the device material when the perovskite layer is thicker than the n-type layer.This results in a longer optical path length for the light within the absorber layer, increasing the probability of photon absorption and the  generation of more charge carriers 41 .Consequently, this leads to an enhancement in cell conversion efficiency.On the contrary, when these values are exceeded by the active layer's depth, the J-V characteristics indicate almost similar efficient devices 40,42 .The advantage of moderate thickness includes a shorter deposition time, lowering the overall process cost.

Effect of defect density states
It is possible to categorize defects in perovskite solar cells as either impurities or interruptions in the pure crystal structure.Since defects emerge during the deposition, or growth routes, material preparation, their inclusion in the construction is inevitable.For more accurate results, numerical modelling of a device involves considering its defect density in the interface or volume.This study investigates the impact of defects states density on PSC  www.nature.com/scientificreports/performance by changing N T from 10 14 to 10 18 cm −3 , representing a range from theoretical device to a heavily tainted material.We have optimized the defect density state of the absorber layer 10 14 cm −343 .As depicted in Fig. 5, the external quantum efficiency of the cell decreases from nearly 99% to 75% as N T increases.This means that just 25% of the light is engaged in the cell structure.Increased bulk non-radiative charge carrier recombination occurs in the absorber layer of cell because of deeper trap sites for charge carriers created by an increase in N T at the bulk and surface defect levels, or grain boundaries.The defects located inside the device structure and materials with defect density up to 10 15 cm −3 can function efficiently.Identifying the tolerance range for impurities in the perovskite layer is crucial for effective functioning, it is pertinent to research including experiments 44 .Moreover, this study aligns with the findings from the literature, indicating that achieving devices with low N T values which is less than 10 14 cm −3 in experiments, is challenging with current production methods.It has been reported N T of 10 14 cm −3 as an optimum value.

Effect of light reflection/transmission at the back/front contact
Overly optimistic simulation of the cell would arise from assuming full transmission of the incoming light flux at the front contact or no light reflection at the interior layers, including the back contact.It is not possible to totally transfer all light into the absorber layer; part of it will always be lost because of absorption in the layers that come before it, including TiO 2 and FTO.The light transmittance can only be accurately modelled at the FTO, serves as the front contact, using SCAPS.
Figure 6a,b show the trends of the J-V and QE properties of the device as the percentage of light transmittance through the front contact varies from 20 to 100%.This feature has a negligible impact on V oc , remaining within the range [1.1; 1.15].However, J sc is significantly affected, dropping from 31.3 to 6.2 mA/cm 2 as the transmission drops from 100 to 20%.Similarly, EQ decreases from 99 to 20%.The production of large charge carriers and, subsequently, the current are affected when the transmission rate drops because fewer photons reach the transmission layer.
Recombination is necessary for the few photogenerated carriers to reach the splitting interface because of the active layer's thickness of 1.6 µm.Reducing the thickness of the absorber layer within the ideal range measured between 1.5 and 1.7 µm is one possible scenario to make up for the limited light transmission via the front layer and contact.Fortunately, a large enough region of the visible spectrum can pass through the absorber layer since the gap between the front window and contact layers is designed to be suitably high (3.2 eV).A device made from non-transparent FTO and ETL materials would exhibit inferior performance.
Furthermore, each inner layer's surface reflects tiny light beams, which begs the question of whether the performance of the cell is directly impacted by this reflected light.Only the reflection % at the back contact is considered by SCAPS.Significant incoming light is trapped by FASnI 3 with a band gap of 1.4 eV.The active layer reabsorbs light that is reflected at the back surface when it escapes and heads towards it.This increases the active layer's absorption capacity and produces more charge carriers, which raise the photogenerated current and, in turn, the cell's overall current.As seen in Fig. 6c,d, which depict the evolution of J-V and QE features, this augmentation is especially noticeable in the present.When the reflection percentage increases from 20 to 100%, V oc stays constant while the current significantly changes from 31 to 32 mA/cm 2 .Better QE is seen in the 700-1000 nm spectral range, which primarily corresponds to the portion of light that was not absorbed during the active layers first trip.
This conclusion is relevant and consistent with earlier studies considering how important it is to build solar cell with reflecting surfaces at the back metal contact 11 .These findings highlight how crucial it is to use materials with maximum transmittance rates in order to maximize solar spectrum transmission.

Effect of metal work function
In perovskite solar cell devices, at least one electrode requires a low work function (WF) to inject or collect charge carriers into the conduction band.To effectively capture holes separated at the FASnI 3 /ETL interface, back metal contacts should have a greater WF.A higher WF of the back contact enhances hole collection efficiency, allowing easy migration from the hole transport layer to the maximum energy level.Nonetheless, electrons must be prevented from passing through the WF of the back metal contact.It was calculated that 4.8 eV would be the ideal WF for metal back contact.
As shown in Fig. 7, the maximum performance of the device was obtained with WF values greater than the value of 4.8 eV.Simulations consistently produced steady results above this threshold value.This is emphasized in Fig. 7, where V oc , J sc , FF and PCE of all remain nearly constant once the WF of the metal contact surpasses 4.8 eV.These results attribute the increased built-in potential to the better V oc and overall efficiency of their PSC device.

Effect of charge carriers' capture cross-sections
In this section, we conducted modelling assuming equal capture cross-sections for electrons and holes (i.e., σ n,p = σ n = σ p ).The numerical analysis focused on different volumetric capture cross-sections at FTO/TiO 2 , TiO /FASnI 3 and FASnI 3 /Cu 2 O interfaces.The effective cross-section of trap levels between the valence and conduction bands that may capture photogenerated carriers at a specific thermal velocity (V th ) is measured by the capture cross-section.
An approximate defect density of 1 × 10 15 cm −3 was taken into account in the volume and at the interfaces, in line with earlier calculations.The numerical simulations were carried out by changing the σ n,p from 1 × 10 16 to 1 × 10 22 cm 245 .As shown in Fig. 8, all photovoltaic output IV parameters are strongly affected by the variation of σ n,p .A smaller σ n,p indicates a more effective structure.According to about mentioned equation of σ n,p , as the σ n,p decreases.Additionally, there is a considerable decrease in Shockley-Read-Hall recombination current, which improves the open-circuit voltage, lowers cell losses, and improves device performance.
Maintaining a constant defect density N T and thermal conditions of simulation (V th = C te ), a reduction in σ n,p leads to a longer lifespan for charge carriers, enhancing their contribution to the photo generation of current.Varying σ n,p from 1 × 10 16 to 1 × 10 22 cm 2 increases V oc from 1.05 to 1.16 V, while the J sc value increases from 29.23 to 31.70 mA/cm 2 .This leads to exceptional results with a PCE of 32.47% and FF of 88.53%.
From literature the authors have achieved the maximum performance of 26.33% with their numerical modelling with 1.0 μm thickness of the device with the σ n,p = 1 × 10 19 cm 246 .Effective passivation at the interface layer can result in small σ n,p , which attenuate bulk defects and minimize grain size variations at thresholds.

Energy band diagram of optimized structure
The transfer of photogenerated charge carriers across the device is demonstrated by charge carrier transport, which is depicted in Fig. 9     and finally to Cu 2 O (E V ~ 0 eV).The formation of a spike between the TiO 2 and FTO impedes the movement of photogenerated electrons toward the front electrode 29,31 .

Conclusion
The FASnI 3 -based perovskite solar cells with an initial structure of maximum performance of 20.95% and FF of 66.40% have been theoretically achieved using SCAPS-1D software.To address industry challenges such as stability, cost efficiency, and more moderate thickness of the device, optimization calculations were conducted by varying material properties in the functional layers, focusing on assessing the impact on output characteristics through J-V and QE analyses.The results demonstrated substantial improvements, and an investigation into the effects of capture cross-sections of the holes and electrons on PV properties led to achieving a PCE of 32.47% and an FF of 88.53% using cell with σ n,p = 1 × 10 22 cm 2 .The optimization approach shows promise, identifying Cu 2 O as a prospective material for stable and highly efficient PSCs, reducing capture cross-sections of electrons and holes through efficient passivation and minimizing defect density.The proposed architecture for future PSCs is Ag/Cu 2 O/FASnI 3 /TiO 2 /FTO.

Figure 1 .
Figure 1.(a) schematic diagram and (b) energy band diagram of FASnI 3 based device structure.

Figure 2 .
Figure 2. The J-V and QE properties of the four HTLs.

Figure 3 .
Figure 3.The J-V characteristics of the PSCs with changing the perovskite layer thickness.

Figure 4 .
Figure 4. Impact of performance layer thickness on device efficiency.

Figure 5 .
Figure 5.Effect defect density state of perovskite layer in PSCs.
of the optimized devices energy level diagram.Electrons can migrate easily from higher to lower energy levels, such as Cu 2 O (E C ~ 2.65 eV) to FASnI 3 (E C ~ [0.5: 1.4 eV]), TiO 2 (E C ~ 0.50 eV), and finally FTO (E C ~ 0.20 eV).Similarly, the valence level arrangement is responsible for successful hole transport: the layer below the most valence-energy-rich layer for practical participation in charge carrier photogeneration.Holes can move freely from FTO (E V ~ − 3.20 eV) to TiO 2 (E V ~ − 3.10 eV), then to FASnI 3 (E V ~ [− 1.3: − 0.15 eV]),

Figure 6 .
Figure 6.The influence of the light reflection/transmission ratio at back/front contact on the performance of FASnI 3 -based PSCs.

Figure 7 .
Figure 7. Output IV parameters of FASnI 3 -based PSCs with the work functions of the metal back contact.

Figure 9 .
Figure 9. Energy band diagram illustrating the Ag/Cu 2 O/FASnI 3 /TiO 2 /FTO structure with the flow of charge carriers.

Table 1 .
input parameters of the initial proposed device.

Table 2 .
input parameters of the different HTLs.

Table 3 .
The comparative performance of devices with different HTLs.